The invention relates to methods and computer-readable media to implement computation of the propagation velocity of seismic waves.
Knowledge of the propagation velocity of seismic waves is required to produce accurate images of underground geology to prospect for oil and gas with the reflection seismic method. The reflection seismic method deploys an array of sound sources (e.g., dynamite, air guns, and vibrating trucks) and receivers (e.g., seismometer or hydrophone) on or below earth's surface to construct an image of underground geology. To gather data to make the image, each sound source produces an explosion or vibration that generates seismic waves that propagate through earth, or initially through water then earth. Underground geologic interfaces, known as “reflectors,” will reflect some energy from the seismic waves back to the receivers. Each receiver will record a “trace” at that time. A multi-channel seismic recording system such as the StrataView manufactured by Geometrics Inc., San Jose, Calif. can be used to collect all of the recorded traces for a given shot. This collection is referred to as a “shot gather.”
To map the underground geology, the recorded time of the shot reflection events of each seismic trace will be mapped to the position at which the reflection occurred, using the propagation velocities of seismic waves, which vary with respect to spatial position. This mapping is known as “prestack depth migration.” Claerbout, Toward a unified theory of reflector mapping, Geophysics v. 36, p. 467 (1971), which is incorporated by reference herein, describes a method of computation known as “downward continuation,” which enables prestack migration. Downward continuation is a computation that mathematically moves the recorded seismic traces and simulated seismic source traces into the subsurface to achieve prestack depth migration.
Downward continuation requires an initial estimate of propagation velocity known as the “migration velocity.” These estimated propagation velocities can be obtained for instance by the method of stacking velocity analysis developed by Taner and Koehler, Velocity spectra—digital computer derivation applications of velocity functions, Geophysics 34, p. 859 (1969), which is incorporated by reference herein.
To form an image from the recorded data at a given depth, downward continuation migration computes the dot product of the downward continued recorded seismic trace and its corresponding downward continued source trace. When an energy peak on the recorded trace is time-coincident with an energy peak on the source trace an image can be formed. This method is known as the “zero time lag correlation imaging condition.” It is noted that the term “lag” is also referred to as “shift.” If the migration velocity matches the true propagation velocity, prestack migration will form an image of the reflector at the correct location. If the migration velocity differs from the true propagation velocity, prestack migration will form an image of the reflector at an incorrect location.
Sava and Fomel, Time-shift imaging condition in seismic migration, Geophysics, v. 71, p. 209 (2006), which is incorporated by reference, state that the zero time lag correlation imaging condition may be generalized to extract energy at a non-zero time lag and used to estimate the propagation velocities. When the migration velocity is incorrect, the energy peak on the downward continued source trace will not match the time of the energy peak on the downward continued recorded trace. By applying the correlation imaging condition at a number of time shifts, other than at zero lag, the amount of misfocusing in time can be computed and related to a velocity error. The generalized imaging condition is known as the “time-shift imaging condition.” For a given position on the recording surface and a given time shift, all the traces are summed. The collection of all these summed traces at that position for all the time shifts is known as “a time-shift gather.”
In regions with significant geologic complexity, velocity analysis using depth migration (MVA) is superior to methods which operate on prestack data. Migration in general, and depth migration in particular, simplify prestack data by correcting for the effects of offset, reflector dip, and propagation from source to receiver in a heterogeneous medium. When the migration velocity is incorrect, migration will incorrectly position the surface data in depth. Some MVA techniques attempt to flatten Kirchhoff common-offset depth migration gathers by measuring depth error as a function of offset and perturbing the migration velocity accordingly.
Kirchhoff offset gathers exhibit artifacts in complex examples, which are not seen in wave equation depth-migrated images, as described in Stolk and Symes, Kinematic artifacts in prestack depth migration, Geophysics v. 69, p. 562 (2004). Claerbout, Imaging the Earth's Interior (1985), which is incorporated by reference herein, devised the zero-time/zero-offset prestack imaging condition which forms the basis of most wave equation MVA techniques. Subsurface offset gathers can be converted to angle gathers by slant-stacking as described by Prucha et al, Angle-domain common image gathers by wave-equation migration, 69th Annual International Meeting, SEG, Expanded Abstracts, p. 824 (1999) and by Sava and Fomel, Angle-domain common-image gathers by wavefield continuation methods, Geophysics v. 68, p. 1065 (2003), and have been used for MVA, as described by Clapp, Incorporating geologic information into reflection tomography, Geophysics v. 69, p. 533, (2004) and by Sava, Migration and velocity analysis by wavefield extrapolation, Ph.D. thesis, Stanford University (2004). However, the slant stack may itself introduce spurious artifacts. Shen et al., Differential semblance velocity analysis by wave-equation migration, SEG Expanded Abstracts, p. 2132 (2003) describe a velocity update method which uses misfocusing in subsurface offset directly.
Another class of MVA methods uses the other wave equation prestack focusing criterion—misfocusing in time—to quantify velocity errors. As described by MacKay and Abma, Imaging and velocity estimation with depth-focusing analysis, Geophysics v. 57, p. 1608 (1992), which is incorporated by reference herein, time-shift gathers can be constructed by phase-shifting source and receiver wave fields in shot record migration. While time-shift gathers can be converted to angle gathers, as described by Sava and Fomel, Time-shift imaging condition in seismic migration, Geophysics, v. 71, p. 209 (2006), which is incorporated by reference herein, MacKay and Abma measured the depth corresponding to best focusing and invoked a relationship attributed to Faye and Jeannot, Prestack migration velocities from focusing analysis, SEG Expanded Abstracts, p. 438 (1986), which is incorporated by reference herein, to relate the measured depth error to a velocity perturbation. The technique has small reflector dip and small offset assumptions. Audebert and Diet, Migrated focus panels: Focusing analysis reconciled with prestack depth migration, SEG Expanded Abstracts, p. 961 (1992), which is incorporated by reference herein, outline an approach to partially overcome these limitations.
In the 1990's, one of the inventors, Dr. Higginbotham, developed a method of computing the propagation velocity of seismic waves in earth. The method assumed a migration velocity, generated time shift gathers using a shot record downward continuation depth migration and the time-shift imaging condition, and converted the time shift gathers to semblance gathers. The energy peaks on the semblance gathers corresponded to the amount of misfocusing in time. The magnitude of the misfocusing in time was used to update the migration velocity. The method incorrectly assumed that a time shift corresponded to zero offset travel time. The method computed inaccurate values of the propagation velocity of seismic waves in the presence of reflector dip and source-receiver offset, and it was not understood how to increase its accuracy.